document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=139052>Question 139052</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Stanbon here are the other two that I needed to repost.  I know it gets late there as I'm in another country, thanks for all of your help, your the best.\r<BR>\n" );
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document.write( "1.  In Utica, Michigan, 205 of 226 school buses passed the annual safety inspection. In Detroit, Michigan, only 151 of 296 buses passed the inspection. <BR>\n" );
document.write( "(a) State the hypotheses for a right-tailed test.<BR>\n" );
document.write( "(b) Obtain a test statistic and p-value. (c) Is normality assured? (d) If significant, is the difference also large enough to be important? \r<BR>\n" );
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document.write( "2.  Prof. Green’s multiple-choice exam had 50 questions with the distribution of correct answers shown below. Research question: At &#945; = .05, can you reject the hypothesis that Green’s exam answers came from a uniform population\r<BR>\n" );
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document.write( "Correct Answer                                  Frequency<BR>\n" );
document.write( "A                                                         8<BR>\n" );
document.write( "B                                                         8<BR>\n" );
document.write( "C                                                         9<BR>\n" );
document.write( "D                                                        11<BR>\n" );
document.write( "E                                                        14<BR>\n" );
document.write( "Total                                                    50<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101437 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=101437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I answered those this morning at 7:00 EST.<BR>\n" );
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document.write( "2. In Utica, Michigan, 205 of 226 school buses passed the annual safety inspection. In Detroit, Michigan, only 151 of 296 buses passed the inspection. <BR>\n" );
document.write( "(a) State the hypotheses for a right-tailed test.<BR>\n" );
document.write( "Ho: p(Ut)-p(Dt)= 0<BR>\n" );
document.write( "Ha: p(Ut)-p(Dt)>0<BR>\n" );
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document.write( "(b) Obtain a test statistic and p-value.<BR>\n" );
document.write( "p-hat(Ut) = 205/226= 0.9071;p-hat(Dt)=0.5101; p(pooled)=(431/522)=0.8257<BR>\n" );
document.write( "z = (9071-0.5101)/[ 0.8257*0.1743/226 + 0.8257*0.1743/296]= 9.6491<BR>\n" );
document.write( "p-value: 2.52x10^-22<BR>\n" );
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document.write( "(c) Is normality assured? <BR>\n" );
document.write( "I'll let you check out those conditions.<BR>\n" );
document.write( "They should be listed in your text.<BR>\n" );
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document.write( "(d) If significant, is the difference also large enough to be important?<BR>\n" );
document.write( "Since p-value is so small the difference is very significant.<BR>\n" );
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document.write( "3. Prof. Green’s multiple-choice exam had 50 questions with the distribution of correct answers shown below. Research question: At &#945; = .05, can you reject the hypothesis that Green’s exam answers came from a uniform population <BR>\n" );
document.write( "Correct Answer Frequency.......Expected<BR>\n" );
document.write( "A ................8................10<BR>\n" );
document.write( "B ................8................10<BR>\n" );
document.write( "C ................9................10<BR>\n" );
document.write( "D ...............11................10<BR>\n" );
document.write( "E ...............14................10<BR>\n" );
document.write( "Total 50 <BR>\n" );
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document.write( "Ho: Observed Frequencies are equal<BR>\n" );
document.write( "Ha; Observed Frequencies are not equal<BR>\n" );
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document.write( "I ran a Chi-Sq Test on a 2x5 matrix with observed in the 1st row and expected in the 2nd row and got the following results:<BR>\n" );
document.write( "Test statistic: Chi-Sq = 1.2114<BR>\n" );
document.write( "p-value: 0.8762<BR>\n" );
document.write( "Meaning: 87.6% of test results could have given stronger evidence for<BR>\n" );
document.write( "rejecting Ho.<BR>\n" );
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document.write( "Conclusion: Since p-value is greater than alpha=5%, Fail to reject Ho.<BR>\n" );
document.write( "The grades follow a uniform distribution.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
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